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Question Number 192917 by BaliramKumar last updated on 31/May/23

Answered by deleteduser1 last updated on 31/May/23

Let tanθ=t,cotθ=c; tc=1 t^2 +c^2 =(t+c)^2 −2tc=(t+c)^2 −2 t^5 +c^5 =(t+c)^5 −5t^4 c−10t^3 c^2 −10t^2 c^3 −5tc^4 ⇒2525=(t+c)^5 −5t^3 −10t−10c−5c^3 =(t+c)^5 −5(t+c)^3 +5(t+c)=2525 t+c=5 works⇒t^2 +c^2 =25−2=23

Lettanθ=t,cotθ=c;tc=1t2+c2=(t+c)2−2tc=(t+c)2−2t5+c5=(t+c)5−5t4c−10t3c2−10t2c3−5tc4⇒2525=(t+c)5−5t3−10t−10c−5c3=(t+c)5−5(t+c)3+5(t+c)=2525t+c=5works⇒t2+c2=25−2=23

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